Among the problems related to filtration and mass transfer in porous bodies, the problems of the adsorption-desorption are currently of the greatest interest. This is due to a wide range of problems: the safety of mining and coal developments, the extraction of combustible gases, the storage of greenhouse gases in formations. At the same time, in theoretical terms, issues related to the multi-scale nature of fractured-porous media, in particular, mining and coal seams, are gaining wide popularity.
This paper considers the problem of filtration flow during gas injection into a porous formation, taking into account gas adsorption both on the surface of channels in macropores and during volumetric sedimentation in micropores. In the paper, it is assumed that the entire pore space of a coal seam, according to the results of recent studies, can be divided into two parts of mutually connected areas that differ from each other in their characteristic sizes of pore channels and, accordingly, with a large difference in permeability. The main attention is paid to the filtration features of the process of adsorbed gas flow in the reservoir. The developed model is based on the theory of inertialess gas motion, i.e. using the Darcy equation written in each zone separately. It is assumed according to the literature that the adsorption process obeys the Langmuir-type equation. The problem considers two stages of the process: gas injection into the reservoir and the process of filtration pressure establishment during reservoir blockage. Pressure changes in two different channel systems are shown depending on the intensity of gas flow from one pore branch of the system to another. With intensive overflows, pressure differences between the areas are insignificant. With weak overflows, the differences are large, which should lead to large internal stresses. The calculations performed qualitatively show the dynamics of the adsorption process during gas movement in the reservoir. It follows from the calculations that it largely depends on the structure of the pore space. With intensive overflows, the adsorption process practically follows the change in pressure in the entire pore space. For weak flows, the resulting large pressure differences between the two regions affect the adsorption process.
